There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ -xln(1 - x)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = -xln(-x + 1)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( -xln(-x + 1)\right)}{dx}\\=&-ln(-x + 1) - \frac{x(-1 + 0)}{(-x + 1)}\\=&-ln(-x + 1) + \frac{x}{(-x + 1)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( -ln(-x + 1) + \frac{x}{(-x + 1)}\right)}{dx}\\=&\frac{-(-1 + 0)}{(-x + 1)} + (\frac{-(-1 + 0)}{(-x + 1)^{2}})x + \frac{1}{(-x + 1)}\\=&\frac{x}{(-x + 1)^{2}} + \frac{2}{(-x + 1)}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{x}{(-x + 1)^{2}} + \frac{2}{(-x + 1)}\right)}{dx}\\=&(\frac{-2(-1 + 0)}{(-x + 1)^{3}})x + \frac{1}{(-x + 1)^{2}} + 2(\frac{-(-1 + 0)}{(-x + 1)^{2}})\\=&\frac{2x}{(-x + 1)^{3}} + \frac{3}{(-x + 1)^{2}}\\ \end{split}\end{equation} \]

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